The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated using a generalized version of Feynman's checkerboard model. They turn out to be closely related to the continuum propagator.
We study a relativistic quantum particle in cosmic string spacetime in the presence of a uniform magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the $su(1,1)$ symmetry. We obtain the energy spectrum and eigenfunctions of this problem by using two algebraic methods: the Schrödinger factorization and the tilting transformation. Finally, we give the explicit form of the relativistic coherent states for this problem.
We build a quantum cellular automaton (QCA) which coincides with 1+1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U(1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut-Susskind staggered version of 1+1 QED. We also show that, in the continuous spacetime limit and in the free one particle sector, it converges to the Dir…
We investigated the effects of the global monopole spacetime on the Dirac and Klein-Gordon relativistic quantum oscillators. In order to do this, we solve the Dirac and Klein-Gordon equations analytically and discuss the influence of this background which is characterized by the curvature of the spacetime on the energy profiles of these oscillators. In addition, we introduce a hard-wall potential and, for a particular case, determine the energy spectrum for relativistic quantum oscillators in this background.
As repeatedly emphasized by Einstein our knowledge of the structure of space and time is based entirely on inferences from observations of physical objects and processes. At the most fundamental level these objects and processes are described by quantum theory. However, the ontological status of the theoretical entities employed by quantum theory is a matter of considerable debate. Furthermore, the nonlocal correlations identified by Bell cannot readily be explained within the standard relativistic framework. This suggests that we should re-examine our understanding of spacetime.
We consider the manner in which the spacetime manifold emerges from a quantum substratum through the transactional process, in which spacetime events and their connections are established. In this account, there is no background spacetime as is generally assumed in physical theorizing. Instead, the usual notion of a background spacetime is replaced by the quantum substratum, comprising quantum systems with nonvanishing rest mass. Rest mass corresponds to internal periodicities that function as internal clocks defining proper times, and in turn, inertial frames that are not themselves aspects o…
The relativistic acceleration of an electron in a uniform gravitational field is calculated numerically using the generalization of the Dirac equation to curved spacetime. Equivalent results are also obtained analytically using an iterative approach that is not based on the WKB approximation, which has been used extensively in the past. The acceleration is found to be proportional to a factor of $(1-3v^2/c^2)$ using Schwarzschild coordinates, which is consistent with the classical geodesic of a particle. These techniques may be useful in resolving the differences between commonly-used approxim…
Relativistic quantum mechanics of a Proca (spin-1) particle in Riemannian spacetimes is constructed. Covariant equations defining electromagnetic interactions of a Proca particle with the anomalous magnetic moment and the electric dipole moment in Riemannian spacetimes are formulated. The relativistic Foldy-Wouthuysen transformation with allowance for terms proportional to the zero power of the Planck constant is performed. The Hamiltonian obtained agrees with the corresponding Foldy-Wouthuysen Hamiltonians derived for scalar and Dirac particles and with their classical counterpart. The unific…
We investigate the analogue effect of the Aharonov-Bohm effect for bound states in two relativistic quantum systems in a spacetime with a space-like dislocation. We assume that the topological defect has an internal magnetic flux. Then, we analyse the interaction of a charged particle with a uniform magnetic field in this topological defect spacetime, and thus, we extend this analysis to the confinement to a hard-wall potential and a linear scalar potential. Later, the interaction of the Klein-Gordon oscillator with a uniform magnetic field is analysed. We first focus on the effects of torsion…
We analyse a relativistic scalar particle with a position-dependent mass in a spacetime with a space-like dislocation by showing that relativistic bound states solutions can be achieved. Further, we consider the presence of the Coulomb potential and analyse the relativistic position-dependent mass system subject to the Coulomb potential in the spacetime with a space-like dislocation. We also show that a new set of relativistic bound states solutions can be obtained, where there also exists the influence of torsion of the relativistic energy levels. Finally, we investigate an analogue of the Ah…
Based on the studies of confinement of quarks, we introduce a linear scalar potential into the relativistic quantum dynamics of a scalar particle. Then, we analyse the linear confinement of a relativistic scalar particle in a Gödel-type spacetime in the presence of a topological defect. We consider a Gödel-type spacetime associated with null curvature, i.e., the Som-Raychaudhuri spacetime, which is characterized by the presence of vorticity in the spacetime. Then, we search for analytical solutions to the Klein-Gordon equation and analyse the influence of the topology of the cosmic string and …
Relativistic quantum metrology studies the maximal achievable precision for estimating a physical quantity when both quantum and relativistic effects are taken into account. We study the relativistic quantum metrology of temperature in (3+1)-dimensional de Sitter and anti-de Sitter space. Using Unruh-DeWitt detectors coupled to a massless scalar field as probes and treating them as open quantum systems, we compute the Fisher information for estimating temperature. We investigate the effect of acceleration in dS, and the effect of boundary condition in AdS. We find that the phenomenology of the…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals classically with motion in space and time. We show here that the mathematical structures of quantum theory and of relativity follow together from pure thought, defined and uniquely constrained by the same elementary "combining and sequencing" symmetries that underlie standard arithmetic and probability. The key is uncertainty, which inevitably accompanies obser…
We propose a fully covariant model for smeared particle detectors in quantum field theory in curved spacetimes. We show how effects related to accelerated motion of the detector and the curvature of spacetime influence the way different observers assign an interaction Hamiltonian between the detector and the field. The fully covariant formulation explicitly leaves the physical predictions of the theory invariant under general coordinate transformations, hence providing a description of particle detector models (e.g., Unruh-DeWitt detectors, models for the light-matter interaction, etc) that is…
Is it possible that two different transitions in the non-relativistic quantum mechanical model of the hydrogen atom give the same frequency? That is, can different energy level transitions in a hydrogen atom have the same photon radiation frequency? This question, which was asked during a Ph.D. oral exam in 1997 at the University of Colorado Boulder, is well-known among physics graduate students. We show a general solution to this question, in which all equifrequency transition pairs can be obtained from the set of solutions of a Diophantine equation. This fun puzzle is a simple yet concrete e…
The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work which is recovered in the nonrelativistic limit. Applying the 3+1-splitting in accordance with the ADM-formalism, we find the relativistic physical momentum operator and compute its standard deviation for wave functions confined to a geodesic ball on a spacelike hypersurface. Its radius can then be understood as a measure of position uncertainty. Under the assumtion of small position unc…
Contractions of the relativistic quantum LCT group and the emergence of spacetime symmetries
Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar)（马达加斯加国家核科学与技术研究所）；Malagasy Academy（马达加斯加科学院）；Faculty of Sciences, iHEPMAD-University of Antananarivo（安塔那那利佛大学理学院）
The spacetime dependence of the inverse temperature four-vector $\boldsymbolβ$ for certain states of the quantized Klein-Gordon field on (parts of) Minkowski spacetime is discussed. These states fulfill a recently proposed version of the Kubo-Martin-Schwinger (KMS) boundary value condition, the so-called "local KMS (LKMS) condition". It turns out that, depending on the mass parameter $m\geq 0$, any such state can be extended either (i) to a LKMS state on some forward or backward lightcone, with $\boldsymbolβ$ depending linearily on spacetime, or (ii) to a thermal equilibrium (KMS) state on all…
Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (a.k.a Hamiltonian-based), pertaining to non-relativistic quantum mechanics. Or they are discrete-spacetime models (a.k.a Quantum Walks or Quantum Cellular Automata-based) enjoying a relativistic continuous spacetime limit. We provide a first example of a quantum simulation scheme that unifies both approaches. The proposed scheme supports both a continuous-time discrete-space limit, leading to lattice fermions, and a continuous-spacetime limit, leading to the Dirac equation. The tra…
Relativistic quantum theories are usually thought of as being quantum field theories, but this is not the only possibility. Here we consider relativistic quantum theories with a fixed number of particles that interact neither through potentials nor through exchange of bosons. Instead, the interaction can occur directly along light cones, in a way similar to the Wheeler-Feynman formulation of classical electrodynamics. For two particles, the wave function is here of the form $ψ(x_1,x_2)$, where $x_1$ and $x_2$ are spacetime points. Specifically, we consider a natural class of covariant equation…
This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with methods of computation are developed in general covariant form for curved phase spaces modelled as cotangent Lorentz bundles. The constructions are based on ideas relating the Grigory Perelman's entropy for geometric flows and associated statistical thermodynamic systems to the quantum von Neumann entropy, classical and quantum relative and conditional entr…
